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This work develops an analytical model of planetary gears and uses it to investigate their natural frequencies and vibration modes. The model admits three planar degrees of freedom for each of the sun, ring, carrier and planets. It includes key factors affecting planetary gear vibration such as gyroscopic effects and time-varying stiffness. For the linear, time-invariant case, examination of the associated eigenvalue problem reveals the well-defined structure of the vibration modes, where the special structure results from the cyclic symmetry of planetary gears. Vibration modes are classified into rotational, translational and planet modes. The unique characteristics of each type of mode are analytically investigated in detail. For each class of mode, reduced-order eigenvalue problems are derived.

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The dynamic response of a helicopter planetary gear system is examined over a wide range of operating speeds and torques. The analysis tool is a unique, semianalytical finite element formulation that admits precise representation of the tooth geometry and contact forces that are crucial in gear dynamics. Importantly, no a priori specification of static transmission error excitation or mesh frequency variation is required; the dynamic contact forces are evaluated internally at each time step. The calculated response shows classical resonances when a harmonic of mesh frequency coincides with a natural frequency. However, peculiar behavior occurs where resonances expected to be excited at a given speed are absent. This absence of particular modes is explained by analytical relationships that depend on the planetary configuration and mesh frequency harmonic. The torque sensitivity of the dynamic response is examined and compared to static analyses. Rotational mode response is shown to be more sensitive to input torque than translational mode response. [S1050-0472(00)00403-7]

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Atmospheric aerosol particles influence climate through their direct and indirect effects. These impacts depend in part on the morphology of the particles, which is determined by their composition. The effect of pH on morphology was investigated using particles composed of 3-methylglutaric acid and ammonium sulfate by manipulating the starting pH of the bulk solution through the addition of aqueous sodium hydroxide. Efflorescence, deliquescence, phase separation, and mixing transitions were observed with optical microscopy. Due to changes in its protonation states, the solubility of the organic component increases with increasing pH, which shifts the location of the separation relative humidity (SRH) from 78.7% for the fully protonated acid to 63.9% for the fully deprotonated acid. Surprisingly, this shift in the SRH leads to hysteresis between the SRH and the mixing relative humidity (MRH). Particle pH has the greatest effect on phase transitions that require nucleus formation, that is, efflorescence and SRH.

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